A rising star of the farm-to-table restaurant world is facing off against an industry titan in a trademark dispute over a simple name: The Kitchen.

The spat pits Kimbal Musk, younger brother of famed entrepreneur Elon Musk, against Wolfgang Puck, whose business empire includes more than a dozen different restaurant concepts, cookbooks, and packaged food and cookware under his brand.

Kimbal Musk started a chain of farm-to-table restaurants 12 years ago called The Kitchen, which now has four locations in Colorado and Chicago, along with a more casual version called The Kitchen Next Door, which has three locations. …

Last summer, Mr. Musk said, he began receiving calls from friends in the hospitality industry asking him if he was planning to open a restaurant in Grand Rapids, Mich. He soon learned that a new restaurant had opened at the Amway Grand Plaza Hotel called The Kitchen By Wolfgang Puck, where the recipes use “only the freshest, locally sourced ingredients,” according to its website.

Mr. Puck also opened a fast-casual restaurant in the same hotel called The Kitchen Counter. The Kitchen By Wolfgang Puck is scheduled to open an outlet in Washington Dulles International Airport in the first half of this year.

As with many trademark disputes, it may come down to who has deeper pockets: Elon Musk’s little brother or a famed celebrity chef.